On Polynomial Space Curves with Flc-frame

Year 2023, Volume: 15 Issue: 2, 414 - 422, 31.12.2023

Mustafa Dede

https://doi.org/10.47000/tjmcs.1127766

Abstract

The first and second derivatives of a curve provide us fundamental
information in the study of the behavior of curve near a point. However,
if a curve is a polynomial space curve of degree n, we don’t know what
is the geometric meaning of the n-th derivative of the curve? There is no
doubt that the Frenet frame is not suitable for this purpose because it is
constructed by using first and second derivatives of a curve. On the other
hand, in this paper by using a new frame called as Flc-frame we are able
to give the geometric meaning of the n-th derivative of a curve. Moreover,
we explore some basic concepts regarding polynomial space curves from
point of view of Flc-frame in three dimensional Euclidean space.

Keywords

Frenet frame, space curve, adapted frame, polynomial curve.

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